Hydrostatic actuators of this species are employed in particular in motor vehicles, and for example for operating brakes such as service brakes and/or parking brakes, parking locks, transmission elements for actuating shifting devices in transmissions such as for example double-clutch transmissions and/or preferentially for actuating one or in the case of a double-clutch transmission two friction clutches, and are known for example from the unpublished German patent applications No. 10 2009 051 245.4 and No. 10 2010 009 297.5. In such hydrostatic actuators, a spindle of the rolling planetary transmission is driven by an electric motor. By means of the planetary body and the ring gear of the rolling planetary transmission, the rotary motion is converted to an axial motion, and a piston of a master cylinder is driven, which acts on the pressurizing agent of a pressure chamber, which transmits the built-up pressure through a pressure line to a pressure chamber of a slave cylinder that is filled with pressurizing medium, whereby a working piston of the slave cylinder is moved axially, which in turn carries out a corresponding actuating work on a brake, friction clutch or the like. For example, by the axial movement of the working piston a brake may be activated or released, or a friction clutch may be engaged or disengaged.